arXiv subjects

B. Kaulakys

Publications and source records attributed to B. Kaulakys.

At least 19 recordsLinked to original sources

arXiv2015

1/f noise from the nonlinear transformations of the variables

The origin of the low-frequency noise with power spectrum $1/f^β$ (also known as $1/f$ fluctuations or flicker noise) remains a challenge. Recently, the nonlinear stochastic differential equations for modeling $1/f^β$ noise have been proposed and analyzed. Here we use the self-similarity properties of this model with respect to the nonlinear transformations of the variable of these equations and show that $1/f^β$ noise of the observable may yield from the power-law transformations of well-known standard processes, like the Brownian motion, Bessel and similar stochastic processes. Analytical and numerical investigations of such techniques for modeling processes with $1/f^β$ fluctuations is presented.

physics.data-an↗

arXiv2015

1/f noise from point process and time-subordinated Langevin equations

Internal mechanism leading to the emergence of the widely occurring 1/f noise still remains an open issue. In this paper we investigate the distinction between internal time of the system and the physical time as a source of 1/f noise. After demonstrating the appearance of 1/f noise in the earlier proposed point process model, we generalize it starting from a stochastic differential equation which describes a Brownian-like motion in the internal (operational) time. We consider this equation together with an additional equation relating the internal time to the external (physical) time. We show that the relation between the internal time and the physical time that depends on the intensity of the signal can lead to 1/f noise in a wide interval of frequencies. The present model can be useful for the explanation of the appearance of 1/f noise in different systems.

cond-mat.stat-mech↗

arXiv2014

Scaling properties of signals as origin of 1/f noise

There are several mathematical models yielding 1/f noise. For example, 1/f spectrum can be obtained from stochastic sequence of pulses having power-law distribution of pulse durations or from nonlinear stochastic differential equations. We show that a couple of seemingly different models exhibiting 1/f spectrum are due to the similar scaling properties of the signals. In addition, we demonstrate a connection between signals with the power-law behavior of the power spectral density generated by the nonlinear stochastic differential equations and modeled by a sequence of random different pulses. An approximation of solutions of the nonlinear stochastic differential equations by the sequence of pulses correctly reproduces the power-law parts of the probability density function and of the power spectral density. This connection provides further insights into the origin of 1/f noise.

cond-mat.stat-mech↗

arXiv2013

Intermittency in relation with 1/f noise and stochastic differential equations

One of the models of intermittency is on-off intermittency, arising due to time-dependent forcing of a bifurcation parameter through a bifurcation point. For on-off intermittency the power spectral density of the time-dependent deviation from the invariant subspace in a low frequency region exhibits 1/\sqrt{f} power-law noise. Here we investigate a mechanism of intermittency, similar to the on-off intermittency, occurring in nonlinear dynamical systems with invariant subspace. In contrast to the on-off intermittency, we consider the case where the transverse Lyapunov exponent is zero. We show that for such nonlinear dynamical systems the power spectral density of the deviation from the invariant subspace can have 1/f^βform in a wide range of frequencies. That is, such nonlinear systems exhibit 1/f noise. The connection with the stochastic differential equations generating 1/f^βnoise is established and analyzed, as well.

nlin.CD↗

arXiv2011

Tsallis distributions and 1/f noise from nonlinear stochastic differential equations

Probability distributions which emerge from the formalism of nonextensive statistical mechanics have been applied to a variety of problems. In this paper we unite modeling of such distributions with the model of widespread 1/f noise. We propose a class of nonlinear stochastic differential equations giving both the q-exponential or q-Gaussian distributions of signal intensity, revealing long-range correlations and 1/f^beta behavior of the power spectral density. The superstatistical framework to get 1/f^beta noise with q-exponential and q-Gaussian distributions of the signal intensity in is proposed, as well.

cond-mat.stat-mech↗

arXiv2011

Herding model and 1/f noise

We provide evidence that for some values of the parameters a simple agent based model, describing herding behavior, yields signals with 1/f power spectral density. We derive a non-linear stochastic differential equation for the ratio of number of agents and show, that it has the form proposed earlier for modeling of 1/f^beta noise with different exponents beta. The non-linear terms in the transition probabilities, quantifying the herding behavior, are crucial to the appearance of 1/f noise. Thus, the herding dynamics can be seen as a microscopic explanation of the proposed non-linear stochastic differential equations generating signals with 1/f^beta spectrum. We also consider the possible feedback of macroscopic state on microscopic transition probabilities strengthening the non-linearity of equations and providing more opportunities in the modeling of processes exhibiting power-law statistics.

nlin.AO↗

arXiv2010

Modeling scaled processes and 1/f^b noise by the nonlinear stochastic differential equations

We present and analyze stochastic nonlinear differential equations generating signals with the power-law distributions of the signal intensity, 1/f^b noise, power-law autocorrelations and second order structural (height-height correlation) functions. Analytical expressions for such characteristics are derived and the comparison with numerical calculations is presented. The numerical calculations reveal links between the proposed model and models where signals consist of bursts characterized by the power-law distributions of burst size, burst duration and the interburst time, as in a case of avalanches in self-organized critical (SOC) models and the extreme event return times in long-term memory processes. The presented approach may be useful for modeling the long-range scaled processes exhibiting 1/f noise and power-law distributions.

nlin.AO↗

arXiv2010

1/f noise from nonlinear stochastic differential equations

We consider a class of nonlinear stochastic differential equations, giving the power-law behavior of the power spectral density in any desirably wide range of frequency. Such equations were obtained starting from the point process models of 1/f^b noise. In this article the power-law behavior of spectrum is derived directly from the stochastic differential equations, without using the point process models. The analysis reveals that the power spectrum may be represented as a sum of the Lorentzian spectra. Such a derivation provides additional justification of equations, expands the class of equations generating 1/f^b noise, and provides further insights into the origin of 1/f^b noise.

nlin.AO↗

arXiv2010

Modeling non-Gaussian 1/f Noise by the Stochastic Differential Equations

We consider stochastic model based on the linear stochastic differential equation with the linear relaxation and with the diffusion-like fluctuations of the relaxation rate. The model generates monofractal signals with the non-Gaussian power-law distributions and 1/f^b noise.

physics.data-an↗

arXiv2010

Point Processes Modeling of Time Series Exhibiting Power-Law Statistics

We consider stochastic point processes generating time series exhibiting power laws of spectrum and distribution density (Phys. Rev. E 71, 051105 (2005)) and apply them for modeling the trading activity in the financial markets and for the frequencies of word occurrences in the language.

physics.data-an↗

arXiv2010

Interaction and chaotic dynamics of the classical hydrogen atom in an electromagnetic field

Expressions for energy and angular momentum changes of the hydrogen atom due to interaction with the electromagnetic field during the period of the electron motion in the Coulomb field are derived. It is shown that only the energy change for the motion between two subsequent passings of the pericenter is related to the quasiclassical dipole matrix element for transitions between excited states.

nlin.CD↗

arXiv2009

Multifractality of the multiplicative autoregressive point processes

Multiplicative processes and multifractals have earned increased popularity in applications ranging from hydrodynamic turbulence to computer network traffic, from image processing to economics. We analyse the multifractality of the recently proposed point process models generating the signals exhibiting 1/f^b noise. The models may be used for modeling and analysis of stochastic processes in different systems. We show that the multiplicative point process models generate multifractal signals, in contrast to the formally constructed signals with 1/f^b noise and signals consisting of sum of the uncorrelated components with a wide-range distribution of the relaxation times.

physics.data-an↗

arXiv2008

Modelling of 1/f noise by sequences of stochastic pulses of different duration

We present and analyze the simple analytically solvable model of 1/f noise, which can be relevant for the understanding of the origin, main properties and parameter dependencies of the flicker noise. In the model, the currents or signals represented as sequences of the random pulses, which recurrence time intervals between transit times of pulses are uncorrelated with the shape of the pulse, are analyzed. It is shown that for the pulses of fixed area with random duration, distributed uniformly in a wide interval, 1/f behavior of the power spectrum of the signal or current in wide range of frequency may be obtained.

physics.data-an↗

arXiv2007

Trading activity as driven Poisson process: comparison with empirical data

We propose the point process model as the Poissonian-like stochastic sequence with slowly diffusing mean rate and adjust the parameters of the model to the empirical data of trading activity for 26 stocks traded on NYSE. The proposed scaled stochastic differential equation provides the universal description of the trading activities with the same parameters applicable for all stocks.

q-fin.TR↗

arXiv2006

Modeling long-range memory trading activity by stochastic differential equations

We propose a model of fractal point process driven by the nonlinear stochastic differential equation. The model is adjusted to the empirical data of trading activity in financial markets. This reproduces the probability distribution function and power spectral density of trading activity observed in the stock markets. We present a simple stochastic relation between the trading activity and return, which enables us to reproduce long-range memory statistical properties of volatility by numerical calculations based on the proposed fractal point process.

physics.soc-ph↗

arXiv2006

Long-range memory model of trading activity and volatility

Earlier we proposed the stochastic point process model, which reproduces a variety of self-affine time series exhibiting power spectral density S(f) scaling as power of the frequency f and derived a stochastic differential equation with the same long range memory properties. Here we present a stochastic differential equation as a dynamical model of the observed memory in the financial time series. The continuous stochastic process reproduces the statistical properties of the trading activity and serves as a background model for the modeling waiting time, return and volatility. Empirically observed statistical properties: exponents of the power-law probability distributions and power spectral density of the long-range memory financial variables are reproduced with the same values of few model parameters.

physics.soc-ph↗

arXiv2006

Quantum Trajectory method for the Quantum Zeno and anti-Zeno effects

We perform stochastic simulations of the quantum Zeno and anti-Zeno effects for two level system and for the decaying one. Instead of simple projection postulate approach, a more realistic model of a detector interacting with the environment is used. The influence of the environment is taken into account using the quantum trajectory method. The simulation of the measurement for a single system exhibits the probabilistic behavior showing the collapse of the wave-packet. When a large ensemble is analysed using the quantum trajectory method, the results are the same as those produced using the density matrix method. The results of numerical calculations are compared with the analytical expressions for the decay rate of the measured system and a good agreement is found. Since the analytical expressions depend on the duration of the measurement only, the agreement with the numerical calculations shows that otherparameters of the model are not important.

quant-ph↗

arXiv2005

1/f Noise in Fractal Quaternionic Structures

We consider the logistic map over quaternions $\mathbb{H}\sim\mathbb{R}^4$ and different 2D projections of Mandelbrot set in 4D quaternionic space. The approximations (for finite number of iterations) of these 2D projections are fractal circles. We show that the point process defined by radiuses $R_j$ of those fractal circles exhibits pure 1/f noise.

math-ph↗